Abstract: Computer analysis of FIM diffusion studies

Abstract

Field ion microscopy has made it possible to observe the diffusion of single atoms or atom clusters at a surface and to examine the interactions between individual atoms. There are two main problems associated with such studies: (1) Only a small number of adatom positions can be recorded per observation, so that statistical fluctuations have a profound effect on the data. (2) The available planes are no larger than 100 Å in diameter, and the effects of the plane boundaries may be significant. We have performed computer simulations1 of the diffusion of one and two adatoms over a surface, both to determine the magnitude of the statistical errors in such experiments and to ascertain the optimal conditions for data collection. In the usual expression for the diffusion coefficient, D= D0 exp(−VD/kT), the activation energy VD can be obtained to ±8%, and the prefactor D0 to an order of magnitude, provided M, the number of diffusion intervals in the Arrhenius plot, amounts to 300. The statistical error in VD can be reduced to 5% with 750 measurements; the error in the prefactor is similarly lowered to a factor of 5. Further increases in M yield only minimal reductions of the statistical error. Simulations were also carried out in order to determine corrections to compensate for the presence of boundaries. The effect of boundaries on the measured values of the mean-square displacement 〈R2〉 is generally approximated by the expression 〈R2〉=2Dτ[1−(4/3a) (4Dτ/π)1/2], which relates the mean-square displacement, executed during an interval τ on a line of length a, to the diffusion coefficient. This is found to be adequate, unless displacements of only one or two steps per diffusion interval predominate. On a plane bounded by a circle of diameter d, this relation becomes 〈R2〉=4Dτ[1−(16/3πd) (4Dτ/π)1/2]. Interactions between adatoms can be deduced from the distribution function governing the distance between two atoms on a surface. Accurate distance measurements on two-dimensional surfaces are difficult. However, for atoms in adjacent one-dimensional channels no such limitation operates. From Monte Carlo simulations it appears that interaction energies can be derived with a standard error of kT/4 provided ?50 pairs per distance are available over the distance range of interest. The most important factor in such measurements is adequate equilibration between observations; atoms should make at least 5 jumps between determinations of interatomic distances to insure meaningful results. These estimates are applied to an analysis of experimental measurements on diffusion and interaction of W2,3 and Ir adatoms4 on the (211) plane of W.